Model Theory by Chang and Keisler references $R(\omega)$ frequently, usually in the context of models $\langle R(\omega), \in\rangle$ of ZF.
What does this notation mean, specifically? From the context, it looks like it's denoting the "usual" sets of ZF, perhaps more formally defined as "All sets reachable by repeated subset/powerset operations with from $\omega$". However, the book never explicitly defines it (or if it does, I missed it).
What's the formal definition of this notation? More importantly, where can I find notation that authors think is common knowledge next time that I miss something while reading a textbook? It's not easy to google $R(\omega)$ and get pertinent results.